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In this paper, optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t-norm is considered as fuzzy composition, and fuzzy inequality replaces ordinary inequality in the constraints. Unlike most optimization algorithms, in fuzzy relational inequalities with fuzzy constraints (FRI-FC) we find a near-feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp (ordinary) inequality constraints. Such solutions are called super-optima in this paper. Subsequently, an algorithm is proposed to find a super-optimum with pre-specified desirable infeasibility. For this purpose, we firstly study some structural properties of the FRI-FC problem and present a new formulization that is independent of t-norms used in the constraints of the problem. This new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters. However, it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super-optimum under a certain sufficient condition. Finally, a modified PSO is presented in which the ability of PSO to solve unconstrained problems with continuous domain, the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized FRI-FC problems. The modified PSO algorithm has been applied to the generalized FRI-FC problem defined with ten well-known continuous t-norms. Additionally, an idea of the FRI-FC problems as outer approximators for FRI problems with ordinary inequalities is also investigated. [ABSTRACT FROM AUTHOR]

Rule learning is a special type of machine learning approaches, and its key advantage is the generation of interpretable models, which provides a transparent process of showing how an input is mapped to an output. Traditional rule learning algorithms are typically based on Boolean logic for inducing rule antecedents, which are very effective for training models on data sets that involve discrete attributes only. When continuous attributes are present in a data set, traditional rule learning approaches need to employ crisp intervals. However, in reality, problems usually show shades of grey, which motivated the development of fuzzy rule learning approaches by employing fuzzy intervals for handling continuous attributes. While a data set contains a large portion of discrete attributes or even no continuous attributes, fuzzy approaches cannot be used to learn rules effectively, leading to a drop in the performance. In this paper, a multi-stage approach of mixed rule learning is proposed, which involves strategic combination of both traditional and fuzzy approaches to handle effectively various types of attributes. We compare our proposed approach with existing algorithms of rule learning. Our experimental results show that our proposed approach leads to significant advances in the performance compared with the existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper we introduce a classifier named TEDAClass (Typicality and Eccentricity based Data Analytics Classifier) which is based on the recently proposed AnYa type fuzzy rule based system. Specifically, the rules of the proposed classifier are defined according to the recently proposed TEDA framework. This novel and efficient systematic methodology for data analysis is a promising addition to the traditional probability as well as to the fuzzy logic. It is centred at non-parametric density estimation derived from the data sample. In addition, the proposed framework is computationally cheap and provides fast and exact per-point processing of the data set/stream. The algorithm is demonstrated to be suitable for different classification tasks. Throughout the paper we give evidence of its applicability to a wide range of practical problems. Furthermore, the algorithm can be easily adapted to different classical data analytics problems, such as clustering, regression, prediction, and outlier detection. Finally, it is very important to remark that the proposed algorithm can work “from scratch” and evolve its structure during the learning process. [ABSTRACT FROM AUTHOR]

This paper investigates the group decision making (GDM) problems with interval-valued Atanassov intuitionistic fuzzy preference relations (IV-AIFPRs) and develops a novel method for solving such problems. A new consistency index of an Atanassov intuitionistic fuzzy preference relation (AIFPR) is introduced to judge the consistency of an AIFPR and then a convergent iterative Algorithm I is designed to repair the consistency of an AIFPR with unacceptable consistency. Subsequently, the consistency and acceptable consistency of an IV-AIFPR are defined through separating an IV-AIFPR into two AIFPRs. Based on Algorithm I, a new iterative Algorithm II is devised to repair the consistency of an IV-AIFPR with unacceptable consistency. Afterwards, to determine decision makers’ (DMs’) weights objectively, an optimization model is established by minimizing the deviations between each individual IV-AIFPR and the collective one. This model is skillfully transformed into a linear goal program to resolve sufficiently considering different principles of decision making. A linear program is built to derive interval-valued Atanassov intuitionistic fuzzy (IVAIF) priority weights of alternatives. Then, a TOPSIS (technique for order performance by similarity to an ideal solution) based approach is proposed to rank such IVAIF priority weights. Thereby, a method for GDM with IV-AIFPRs is put forward. At length, a practical example of a virtual enterprise partner selection is provided to illustrate the feasibility and validity of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to attempt to propose a method based on evidential reasoning for hybrid grey attribute decision-making problems where the attribute weights are partially known, in which the attribute values are interval grey numbers and linguistic grades. Design/methodology/approach – The method is that the decision-maker gives whitenization of each interval grey number based on their preference and belief structure of the form of qualitative attribute values, whitenization of quantitative attributes can be equivalently expressed in the form of belief structure with the principle of utility value equivalence, and then the grade belief structure decision matrix can be determined. By using the analytical evidential reasoning algorithm, belief degrees of each alternative belonging to each linguistic grade are obtained. Two pairs of nonlinear optimization models which are solved by genetic algorithms (GA) are constructed to compute the maximum and the minimum expected utilities of each alternative, respectively. Findings – The results show that decision-maker based on his/her risk preference gives whitenization of each interval grey number and selects corresponding alternative policy. Practical implications – The method exposed in the paper can be used to deal with problems of grey multiple attribute decision making and hybrid grey multiple attribute decision making. Originality/value – The paper succeeds in constructing two pairs of nonlinear optimization models based on the analytical evidential reasoning algorithm which are solved by genetic algorithms and the hybrid grey multiple attribute decision-making approach with partial weight information. [ABSTRACT FROM AUTHOR]